There may be some versions with minor differences to a motherboard as
Microsoft tries to thwart users and particularily installers of hardware
mod-chips, but many of these really have little effect on soft-modding.

Xbox Differences

Motherboard model

In general, the different versions of an Xbox refer to different versions of
the motherboard layout and/or the things on the motherboard (video
encoding chip, power connector style, fan or heat sink on GPU).

There appears to not be a major difference between 1.2 and 1.3, as
Xbox-Scene's tutorial on identifying an Xbox version says to check
Xbox-Linux's
Versions Finding page and looking at a serial number, and that
"There's no perfect method to see the difference between v1.2 and
v1.3 (yet)." There must be some difference, though, since the
Xbox hacking community seems to be in agreement in calling these
things different versions. "We do know that all PAL Special
Edition translucent green xbox consoles (not the new NTSC Special
Edition Halo xboxes) are still v1.2."

1.4/1.5

The 1.4/1.5 Xboxes use the Focus video encoding chip. The difference
between the 1.4 and 1.5 is that the "LPC 3.3v/ground is
disconnected" on the 1.5, but Microsoft seems to have disfavored
the 1.5 and stopped manufacturing them, instead making version 1.4
Xboxes again until 1.6 came out.

1.6

The 1.6 Xboxes use the "xcalibur" video encoding chip, which
is most easily identified by having an Xbox logo on it, whereas other
video encoding chips had large names of the previous video encoding
chip manufacturers.

Information on what version your Xbox is can be found at
http://www.xbox-scene.com/versions_0.php
One of the most important differences is whether an Xbox is version 1.0 (if
last four digits of the serial number are 03, or if the last four digits
of the serial number are 02 and the manufacturing date is November 2002 or
earlier), or any later version (if it is not a 1.0 Xbox using the
information just described), because all later versions use the same RC4
Key but that is different than the RC4 Key that version 1.0 uses.

RC4 Key/EEPROM Key

The most important difference for soft modders may be the RC4 Key/EEPROM
key, which hasn't changed frequently but there are a few different ones that
Microsoft has used. If some software says an Xbox is a 1.1 Xbox that may
actually just be referring to the EEPROM key being used, and the Xbox may be
a later version, possibly as late as 1.5.

DVD Drive

What DVD drive do I have?, Samsung, Philips or Thomson?
The three drives, as pictured on the URL linked to, are Thomson, Samsun, and
Philips. Thomson has a simple U-shaped hole in the tray, being circular in
the middle and going back to the system. The outer and inner rings of the
plastic on the tray are about the same size. Comments on that page suggest
it is the best one at reading different disc types like DVD+R discs,
although the opinions do seem to vary widely. A
drive by Phillips has a bit more of a
keyhole-shaped hole, with a larger circular hole in the middle of the tray,
and the circular portion of the hole is wider than some of the rest of the
hole which goes back towards the system. The inner ring of plastic is
fairly small. Another drive is one made by Samsung, and it has two extra
holes in the tray under where the disc would go, as well as a couple of
additional holes in the plastic towards the outside of the system.